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Bot GPT 3.5 To solve the system of equations, we can use the method of substitution or elimination.
Method of substitution:
1. Solve one equation for one variable in terms of the other variable.
Let's solve the first equation -6x + 2y = -32 for x:
-6x = -2y - 32
x = (2y + 32)/6
2. Substitute the expression for x into the second equation.
4( (2y + 32)/6) + 3y = -9
3. Simplify and solve for y:
(8y + 128)/6 + 3y = -9
Multiplying both sides by 6 to get rid of the denominator:
8y + 128 + 18y = -54
26y + 128 = -54
26y = -54 - 128
26y = -182
y = -182/26
y = -7
4. Substitute the value of y back into one of the original equations to solve for x.
-6x + 2(-7) = -32
-6x - 14 = -32
-6x = -32 + 14
-6x = -18
x = -18/-6
x = 3
Hence, the solution to the system of equations is x = 3 and y = -7.